Barth, KF, Rippon, PJ and Sixsmith, DJ 
ORCID: 0000-0002-3543-6969
(2017)
The MacLane class and the Eremenko-Lyubich class.
Annales Academiae Scientiarum Fennicae. Mathematica, 42 (2).
pp. 859-873.
(In Press)
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Abstract
In 1970 G. R. MacLane asked if it is possible for a locally univalent function in the class $\mathcal{A}$ to have an arc tract. This question remains open, but several results about it have been given. We significantly strengthen these results, in particular replacing the condition of local univalence by the more general condition that the set of critical values is bounded. Also, we adapt a recent powerful technique of C. J. Bishop in order to show that there is a function in the Eremenko-Lyubich class for the disc that is not in the class $\mathcal{A}$.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | math.CV, math.CV, 30D40 |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 07 Apr 2017 08:33 |
| Last Modified: | 19 Jan 2023 07:06 |
| DOI: | 10.5186/aasfm.2017.4252 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3006830 |
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